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Suppose that n = 7. PART I Let a 40. What is a mod n? Let b 6. What is b mod n? Let c =37. What is c mod n? Let d =32. What is d mod n? Let e 38. What is e mod n? PART II Fill in the following multiplication table mod 7: aa mod 7 = mod 7 = 00000 ca mod 7 = mod 7 = ac mod 7 = cc mod 7 = ae ce

Suppose that n = 7. PART I Let a 40. What is a mod n? Let b 6. What is b mod n? Let c =37. What is c mod n? Let d =32. What is d mod n? Let e 38. What is e mod n? PART II Fill in the following multiplication table mod 7: aa mod 7 = mod 7 = 00000 ca mod 7 = mod 7 = ac mod 7 = cc mod 7 = ae ce

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 3TFE: Label each of the following statements as either true or false. a2b2(modn) and implies ab(modn) or...
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I want to get answer of 4parts.

Suppose that n = 7. PART I Let a 40. What is a mod n? Let b 6. What is b mod n? Let c =37. What is c mod n? Let d =32. What is d mod n? Let e =38. What is e mod n? PART II Fill in the following multiplication table mod 7: aa mod 7 = mod 7 = ca mod 7 = 40 mod 7 = ea mod 7 = mod 7 = ac mod 7 = cc mod 7 = ec mod 7 = ae ce ee
Transcribed Image Text:Suppose that n = 7. PART I Let a 40. What is a mod n? Let b 6. What is b mod n? Let c =37. What is c mod n? Let d =32. What is d mod n? Let e =38. What is e mod n? PART II Fill in the following multiplication table mod 7: aa mod 7 = mod 7 = ca mod 7 = 40 mod 7 = ea mod 7 = mod 7 = ac mod 7 = cc mod 7 = ec mod 7 = ae ce ee
PART III Using your results in Part I, fill in the following multiplication table mod 7: (a mod 7 )(c mod 7 ) mod 7 = (a mod 7 )(a mod 7 ) mod 7 = = (c mod 7 )(a mod 7 ) mod 7 = (e mod 7 )(a mod 7 ) mod 7 = = (c mod 7 )(c mod 7 ) mod 7 = (e mod 7 )(c mod 7 ) mod 7 = (a mod 7 )(e mod 7 ) mod 7 (c mod 7 )(e mod 7 ) mod 7 = (e mod 7 )(e mod 7 ) mod 7 PART IV Consider your answers from Parts II and III. Can you make a conjecture relating them? Write it in the box below.
Transcribed Image Text:PART III Using your results in Part I, fill in the following multiplication table mod 7: (a mod 7 )(c mod 7 ) mod 7 = (a mod 7 )(a mod 7 ) mod 7 = = (c mod 7 )(a mod 7 ) mod 7 = (e mod 7 )(a mod 7 ) mod 7 = = (c mod 7 )(c mod 7 ) mod 7 = (e mod 7 )(c mod 7 ) mod 7 = (a mod 7 )(e mod 7 ) mod 7 (c mod 7 )(e mod 7 ) mod 7 = (e mod 7 )(e mod 7 ) mod 7 PART IV Consider your answers from Parts II and III. Can you make a conjecture relating them? Write it in the box below.
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